相关论文: Conformal Properties and Baecklund Transform for t…

Integrable equations with second order Lax pair like KdV and Camassa-Holm (CH) exhibit interesting conformal properties and can be written in terms of the so-called conformal invariants (Schwarz form). These properties for the CH hierarchy…

It is well known that the Camassa-Holm equation possesses numerous remarkable properties characteristic for KdV type equations. In this paper we show that it shares one more property with the KdV equation. Namely, Ibragimov has shown that…

This work deals with the conformal transformations in six-dimensional spinorial formalism. Several conformally invariant equations are obtained and their geometrical interpretation are worked out. Finally, the integrability conditions for…

In this article we review the Duistermaat-Heckman integration formula and the ensuing equivariant cohomology structure, in the finite dimensional case. In particular, we discuss the connection between equivariant cohomology and classical…

We study examples where conformal invariance implies rational critical indices, triviality of the underlying quantum field theory and emergence of hypergeometric functions as solutions of the field equations.

We study the symmetry and integrability of a modified Camassa-Holm Equation (MCH), with an arbitrary parameter $k,$ of the form $$u_{t}+k(u-u_{xx})^2u_{x}-u_{xxt}+(u^{2}-{u_{x}}^2)(u_{x}-u_{xxx})=0.$$ By using Lie point symmetries we reduce…

We consider the algebraic setting of classical defects in discrete and continuous integrable theories. We derive the "equations of motion" on the defect point via the space-like and time-like description. We then exploit the structural…

We consider here two discrete versions of the modified KdV equation. In one case, some solitary wave solutions, B\"acklund transformations and integrals of motion are known. In the other one, only solitary wave solutions were given, and we…

We study numerical computation of several conformal invariants of simply connected domains in the complex plane including, the hyperbolic distance, the reduced modulus, the harmonic measure, and the modulus of a quadrilateral. The method we…

We study the breakdown of conformal symmetry in a conformally invariant gravitational model. The symmetry breaking is introduced by defining a preferred conformal frame in terms of the large scale characteristics of the universe. In this…

We construct a new series of multicomponent integrable PDE systems that contain as particular example (with appropriately chosen parameters) many famous integrable systems including KdV, coupled KdV, Harry Dym, coupled Harry Dym,…

Using geometrical approach exposed in arXiv:math/0304245 and arXiv:nlin/0511012, we explore the Camassa-Holm equation (both in its initial scalar form, and in the form of 2x2-system). We describe Hamiltonian and symplectic structures,…

Series of deformed Camassa-Holm-type equations are constructed using the Lagrangian deformation and Loop algebra splittings. They are weakly integrable in the sense of modified Lax pairs.

We study 2D discrete integrable equations of order 1 with respect to one independent variable and $m$ with respect to another one. A generalization of the multidimensional consistency property is proposed for this type of equations. The…

We study the relevance of various scalar equations, such as inviscid Burgers', Korteweg-de Vries (KdV), extended KdV, and higher order equations (of Camassa-Holm type), as asymptotic models for the propagation of internal waves in a…

Recently the associated Camassa-Holm (ACH) equation, related to the Fuchssteiner-Fokas-Camassa-Holm equation by a hodograph transformation, was introduced by Schiff, who derived B\"{a}cklund transformations by a loop group technique and…

We discuss the possible relationship between geodesic flow, integrability and supersymmetry, using fermionic extensions of the KdV equation, as well as the recently introduced supersymmetrisation of the Camassa-Holm equation, as…

We study a class of 1+1 quadratically nonlinear water wave equations that combines the linear dispersion of the Korteweg-deVries (KdV) equation with the nonlinear/nonlocal dispersion of the Camassa-Holm (CH) equation, yet still preserves…

We introduce a new integrable equation valued on a Cayley-Dickson (C-D) algebra. In the particular case in which the algebra reduces to the complex one the new interacting term in the equation cancells and the equation becomes the known…

It is known that some cosmological perturbations are conformal invariant. This facilitates the studies of perturbations within some gravitational theories alternative to general relativity, for example the scalar-tensor theory, because it…